## What is Semi-Annual Compounding on a Mortgage…

In a prior article, I explained that mortgages in Canada will have their rates quoted on a SEMI-ANNUAL compounding basis. Most other countries quote the rate on a monthly basis, and despite being in the industry, I have trouble wrapping my own head around what this semi-annual business means, and after discussing this with accountants, financial planners, and other brokers, it became clear that a write-up of how it works versus the more common monthly and annual compounding would be instructive.

This is a technical article that will go through the nuts and bolts of interest calculation. While it is not exactly fun stuff, it will serve to clarify the difference between the three most common forms of interest and the effect that each has on what you ACTUALLY pay on your mortgage. Ultimately, the rate on a mortgage is not as important as the dollars and cents that you have to pay.

All examples below will follow the same structure and will have the following assumptions:

1. Principle amount borrowed is $100,000

2. Interest rate used will be 10% (annually, monthly, and semi-annually)

3. No Payments will be made (so we can isolate the effect of the interest and its compounding)

4. All money is borrowed on January 1st and repaid on December 31st for ease of comparison

5. All numbers rounded to the nearest 1 dollar for ease of reading and presentation

**ANNUAL COMPOUNDING**

This is the most common form of interest in the consumer eyes, but in reality is not that common in the mortgage world. This form of compounding is the lowest overall EFFECTIVE rate (the rate you are really paying), and therefore it is the way that banks pay YOU such as on a term deposit or GIC.

Taking the numbers from above, here is how the interest would accrue and compound on an annual basis.

January $100,000 Outstanding

February $100,000 Outstanding

March $100,000 Outstanding

April $100,000 Outstanding

May $100,000 Outstanding

June $100,000 Outstanding

July $100,000 Outstanding

August $100,000 Outstanding

September $100,000 Outstanding

October $100,000 Outstanding

November $100,000 Outstanding

December $100,000 Outstanding + $10,000 Annual Interest Accrued and Compounded

Total $110,000

**Interest Accrued is $10,000**

This type of interest is typically called SIMPLE interest as it is a relatively easy concept to understand and calculate.

**MONTHLY COMPOUNDING**

The next most common form of compounding is the monthly compounding which is used on nearly all consumer loans, credit cards, student loans, retail cards, car loans, lease payments, and just about every other form of credit. It is relatively easy to wrap the mind around, but we will work through the numbers anyways to show how it is actually a higher rate of interest than the previous semi-annual compounding.

Taking the numbers from above, here is how the interest would accrue and compound.

January $100,000 Outstanding +$833 of monthly compounded interest

February $100,833 Outstanding +$840 of monthly compounded interest

March $101,673 Outstanding +$847 of monthly compounded interest

April $102,520 Outstanding +$854 of monthly compounded interest

May $103,374 Outstanding +$861 of monthly compounded interest

June $104,235 Outstanding +$869 of monthly compounded interest

July $105,104 Outstanding +$876 of monthly compounded interest

August $105,980 Outstanding +$883 of monthly compounded interest

September $106,863 Outstanding +$890 of monthly compounded interest

October $107,753 Outstanding +$898 of monthly compounded interest

November $108,651 Outstanding +$905 of monthly compounded interest

December $109,556 Outstanding + $913 of monthly compounded interest

Total $110,469

**Interest Accrued is $10,469**

As you can see from the two examples above, the monthly compounding results in $469 more interest paid than the annual compounding despite having the SAME QUOTED RATE of 10%!!! This is JUST the result of more frequent compounding. By compounding, I am referring to the banks calculating the interest, adding it to the principle, and then recalculating next months interest based on the new higher amount. In other words, the interest ON the interest. The more frequent the compounding (monthly vs annually) the higher amount you will ultimately pay in dollars and cents.

**SEMI-ANNUAL COMPOUNDING**

So if monthly compounding works out to being a higher amount of interest paid than annually compounding, semi-annual compounding (once every 6 months) should work out to be higher than annual compounding, but lower than monthly compounding.

Let us see if the math works out that way.

January $100,000 Outstanding

February $100,000 Outstanding

March $100,000 Outstanding

April $100,000 Outstanding

May $100,000 Outstanding

June $100,000 Outstanding + $5,000 semi-annual interest accrued and compounded

July $105,000 Outstanding

August $105,000 Outstanding

September $105,000 Outstanding

October $105,000 Outstanding

November $105,000 Outstanding

December $105,000 Outstanding + $5,250 Interest Accrued and Compounded

Total $110,250

**Interest Accrued is $10,250**

In summary, the amount of interest paid under each type of compounding is as follows:

$10,000 Annual Compounding

$10,250 Semi-Annual Compounding

$10,469 Monthly Compounding

…and if we take it a step further…

$10,516 Daily Compounding

The bottom line is that the more frequent the compounding periods, the more interest you will actually pay despite the fact that it still just says 10%.

If you really want to make yourself crazy, go look at your term deposits or GICs and then look at your credit cards… you will find that your term deposits (when the bank pays YOU) the interest is calculated annually in most cases, and that your credit cards (when you pay the BANK) are compounded monthly (or maybe even daily!!!). Just one more way that the bank always wins…